Overflow is a board game for two players or one player against the computer. Somebody may remember Atoms for the Amiga where you had to set off chain reactions to win the other player's pieces. Well, this is basically the same theme, except that the pieces are not spinning atoms. The rules are very simple, but playing the game is not at all easy.
GNU Chess lets most modern computers play a full game of chess. It has a plain terminal interface but supports visual interfaces such as X-Windows "xboard".
A multi-player networked clone of the classical Bubble Bobble board game. Throw bubbles at monsters and collect dozens of different bonuses before your co-players!
The basic aim is to collect all the money by extending Komi the Space Frog's tongue, while avoiding the bad guys. Komi's spiritual predecessor is an old Spectrum game called Glug Glug which had similar(ish) gameplay.